How to bevel something on only some faces?
Its sort of unavoidable.  You'll need to transition from the single edge (above) to the split/beveled edge (below) somehow.
If you want the bevel to only be on the vertical part, you can add an edge loop (highlighted) just below the current knee joint, and then select the edge below the edge loop and just bevel that. Then the 'fan' that transitions from no-bevel to bevel will be on the vertical edge.